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Understanding Equations
Understanding Equations 2
Interpret
Word Problems
Essential Questions
100
Identify the slope and the y-intercept of the following equation: y = 2x - 3
m = 2 or 2/1 b = -3 or (0, -3)
100
Identify the slope and the y-intercept of the following equation: y = -1/4x
m = -1/4 b = 0 or (0, 0)
100
The equation below represents a car's distance in miles vs. time (in hours). y = 62x What is the car's speed?
62 miles per hour
100
Steph owes her mom money. Steph pays her mom back the same amount each week. After one week she owes $18 and after two weeks only owes $15. Find and interpret the rate of change.
rate of change: 3 or 3/1 Steph pays her mom back $3 every week.
100
What is a function?
Possible Answers: Each input (x) has only ONE output (y). Therefore, the x-values do not repeat. The graph passes the vertical line test.
200
Find the y-intercept of the following equation: 2x - 4y = 20
y-int: -5 or (0, -5)
200
Find the x-intercept of the following equation: y = 2x + 18
x-int: -9 or (-9, 0)
200
Dodge got a Wendy's gift card for his birthday. He spends the same amount of money per week to buy food. Week 0, $20 left on Gift Card Week 1, $16.50 left on Gift Card Week 2, $13.00 left on Gift Card, etc. Would the slope of this line be positive or negative? Explain.
The slope would be negative, because it represents how much Dodge spends each week that he goes to Wendy's. Each week, he has $3.50 less on the card.
200
Steph owes her mom money. Steph pays her mom back the same amount each week. After one week she owes $18 and after two weeks only owes $15. Find and interpret the initial value.
21 Steph originally owes her mom $21.
200
Does (0, 2) (1, 4) (2, 6) (3, 8) represent a function? Explain.
Yes, the x-values do not repeat, therefore a function.
300
Find the x-intercept of the following equation: -3x + 8y = -36
x-int: 12 or (12, 0)
300
Find the x- & y- intercepts of the following equation: -4x + 3y = 12
x-int: -3 or (-3, 0) y-int: 4 or (0, 4)
300
Casey got a box of chocolates to celebrate finishing SBAC. She already ate 3 pieces of chocolate, and she plans on having 1 piece per night. Write an equation to represent the total amount of chocolates in the box.
y = x + 3 or y = 1x + 3
300
Write a function rule for this statement: the output is 1 more than half the input.
y = 1/2x + 1
300
What does the graph of a linear equation represent?
The graph of a linear equation represents all possible solutions to the equation.
400
Write the equation 2x - 3y = -6 in slope-intercept form.
y = 2/3x + 2
400
Write the equation 3x - y = 5 in slope-intercept form.
y = 3x - 5
400
Dodge got a Wendy's gift card for his birthday. He spends the same amount of money per week to buy food. Week 0, $20 left on Gift Card Week 1, $16.50 left on Gift Card Week 2, $13.00 left on Gift Card, etc. Write an equation to represent the total amount of money remaining on the gift card.
y = -3.5x + 20 or y = 20 - 3.5x
400
Casey got a box of chocolates to celebrate finishing SBAC. She already ate 3 pieces of chocolate, and she plans on having 1 piece per night. Would the slope of this line be positive or negative? Explain.
The slope would be positive, because it represents the piece of chocolate Casey eats per night.
400
What are the different ways that you could represent a linear function?
A linear function can be represented as... - a straight line - a table with a constant rate of change - an equation (in slope-intercept, standard, or point-slope form)
500
Write a function rule for this statement: the output is 3 less than two times the input.
y = 2x - 3
500
Is the ordered pair (-2, -6) a solution to the function y = 3/2x - 2?
y = 3/2(-2) - 2 y = -3 - 2 y = -5 (NOT -6!) No, the ordered pair (-2, -6) is not a solution, but (-2, -5) is.
500
(-2, 5) (-1, 3) (0, 1) (1, -1) Write an equation for the linear function above. Identify the slope and the y-intercept.
y = -2x + 1 m = -2 or -2/1 b = 1 or (0,1)
500
Steph owes her mom money. Steph pays her mom back the same amount each week. After one week she owes $18 and after two weeks only owes $15. Write an equation that represents this linear function.
y = -3x + 21 or y = 21 - 3x
500
(-2, 4) (-1, 2) (0, 0) (1, -2) (2, -4) Does the table of values represent a function? If so, is it linear? Explain.
Yes it is a function, no x-values repeat. It is also linear, because it has a constant rate of change of -2/1. (y decreases by 2 as x increases by 1)